Size-dependent fracture behavior of quasi-Brittle materials: A peridynamic approach within Ansys LS-DYNA

The transition from toughness-controlled to strength-controlled fracture with changing specimen size − known as the size effect (SE) − is a key feature of quasi-brittle materials. While widely investigated through experiments and conventional numerical models, studies employing Peridynamics (PD) to capture this phenomenon remain scarce and often yield limited accuracy. This work addresses that gap by analyzing the size-dependent fracture behavior of quasi-brittle materials using Bond-Based (BB) PD theory implemented with native elements in Ansys LS-DYNA (PD-DYNA). A novel combination of a bilinear PD model, a 3D stochastic field to represent material heterogeneity, a spatial attenuation kernel, and a discretized micro-modulus function is proposed. The model is validated against two experimental campaigns involving three-point bending tests on notched concrete beams under both mode-I and mixed-mode conditions. Simulations successfully reproduce peak loads, softening behavior, and kinked crack paths observed experimentally. To quantify the scale effect, a fractal-based framework is employed, enabling a consistent interpretation of the mechanical response across specimen sizes. The results demonstrate that the proposed PD-DYNA model can accurately capture the size effect in quasi-brittle fracture, overcoming limitations of earlier PD approaches and validating the potential of fractal-based analysis in PD modeling.